Vibronic coupling and double excitations in linear response time-dependent density functional calculations: Dipole-allowed states of N2

Nonadiabatic couplings from time-dependent density functional theory: Formulation in the Casida formalism and practical scheme within modified linear response

We present an efficient method to compute nonadiabatic couplings (NACs) between the electronically ground and excited states of molecules, within the framework of time-dependent density functional theory (TDDFT) in frequency domain. Based on the comparison of dynamic polarizability formulated both in the many-body wave function form and the Casida formalism, a rigorous expression is established for NACs, which is similar to the calculation of oscillator strength in the Casida formalism. The adiabatic local density approximation (ALDA) gives results in reasonable accuracy as long as the conical intersection (ci) is not approached too closely, while its performance quickly degrades near the ci point. This behavior is consistent with the real-time TDDFT calculation. Through the use of modified linear response theory together with the ground-state-component separation scheme, the performance of ALDA can be greatly improved, not only in the vicinity of ci but also for Rydberg transitions and charge-transfer excitations. Several calculation examples, including the quantization of NACs from the Jahn-Teller effect in the H3 system, have been given to show that TDDFT can efficiently give NACs with an accuracy comparable to that of wave-function-based methods.

Vibronic structure of the permanganate absorption spectrum from time-dependent density functional calculations

The UV absorption spectrum of the permanganate anion is a prototype transition-metal complex spectrum. Despite this being a simple d0 Td system, for which a beautiful spectrum with detailed vibrational structure has been available since 1967, the assignment of the second and third bands is still very controversial. The issue can be resolved only by an elucidation of the intricate vibronic structure of the spectrum. We investigate the vibronic coupling by means of linear-response time-dependent density functional calculations. By means of a diabatizing scheme that employs the transition densities obtained in the TDDFT calculations in many geometries around Re, we construct a Taylor series expansion in the normal coordinates of a diabatic potential energy matrix, coupling 24 excited states. The simulated vibronic structure is in good agreement with the experimental absorption spectrum after the adjustment of some of the calculated vertical excitation energies. The peculiar blurred vibronic structure of the second band, which is a very distinctive feature of the experimental spectrum, is fully reproduced in the calculations. It is caused by the double-well shape of the adiabatic energy surface along the Jahn-Teller active e mode of the allowed 1E state arising from the second 1T2 state, which exhibits a Jahn-Teller splitting into 1B2 and 1E states. We trace the double-well shape to an avoided crossing between two diabatic states with different orbital-excitation character. The crossing can be explained at the molecular orbital level from the Jahn-Teller splitting of the set of 7t2{3d(xy), 3d(xz), 3d(yz)} orbitals (the LUMO + 1), to which the excitations characterizing the diabatic states take place. In contrast to its character in the two well regions, at Re the 2(1)T2 state is not predominantly an excitation to the LUMO + 1, but has more HOMO - 1 --> LUMO (2e = {3d(x2-y2), 3d(z2)}) character. The changing character of the 2(1)T2 - 1E state along the e mode implies that the assignment of the experimental bands to single orbital transitions is too simplistic intrinsically. This spectrum, and notably the blurring of the vibronic structure in the second band, can be understood only from the extensive configurational mixing and vibronic coupling between the excited states. This solves the long-standing assignment problem of these bands.

Vibronic coupling in the excited cationic states of ethylene: simulation of the photoelectron spectrum between 12 and 18 eV

The effect of vibronic coupling on structure and spectroscopy is investigated in the excited cationic states of ethylene. It is found from equation of motion coupled cluster singles and doubles method for ionization potential electronic structure calculations in a triple-zeta plus double polarization basis set that ethylene in its third (B (2)A(g)) and fourth (C (2)B(2u)) ionized states does not have a stable minimum-energy geometry. The potential-energy surfaces of these states are energetically distinct and well separated at the ground-state geometry of ethylene, but in a geometry optimization as the structure of the ion relaxes, these surfaces end up in conical intersections and finally in the stable equilibrium geometry of the second ionized state (A (2)B(3g)). The topology of the potential-energy surfaces can be clearly understood using a vibronic model Hamiltonian. Furthermore, by diagonalizing this model Hamiltonian, the photoelectron spectrum of ethylene corresponding to the second, third, and fourth ionized states (12-18 eV) is simulated. Spectra from vibronic simulations including up to quartic coupling constants and using various normal-mode basis sets are compared to those from vertical Franck-Condon simulations to understand the importance of vibronic coupling and nonadiabatic effects and to examine the influence of individual normal modes on the spectrum.

Comparison of frozen-density embedding and discrete reaction field solvent models for molecular properties

We investigate the performance of two discrete solvent models in connection with density functional theory (DFT) for the calculation of molecular properties. In our comparison we include the discrete reaction field (DRF) model, a combined quantum mechanics and molecular mechanics (QM/MM) model using a polarizable force field, and the frozen-density embedding (FDE) scheme. We employ these solvent models for ground state properties (dipole and quadrupole moments) and response properties (electronic excitation energies and frequency-dependent polarizabilities) of a water molecule in the liquid phase. It is found that both solvent models agree for ground state properties, while there are significant differences in the description of response properties. The origin of these differences is analyzed in detail and it is found that they are mainly caused by a different description of the ground state molecular orbitals of the solute. In addition, for the calculation of the polarizabilities, the inclusion of the response of the solvent to the polarization of the solute becomes important. This effect is included in the DRF model, but is missing in the FDE scheme. A way of including it in FDE calculations of the polarizabilities using finite field calculations is demonstrated.

Calculation of Ionization Potentials of Small Molecules: A Comparative Study of Different Methods

With the help of various theoretical methods, ionization potentials (IPs) have been computed for a panel of small molecules containing atoms of group 14, 15, or 16 and representing different singly, doubly, or triply bonded systems with or without an interacting heteroatom lone pair. Comparison of experimental IP values to theoretical results indicates that (i) the standard outer valence green function (OVGF), density functional theory (DFT), and DeltaSCF methods lead to rather accurate values, (ii) the CASPT2 method systematically underestimates IPs, (iii) the method of deducing IPs from a shift of some standard DFT eigenvalue spectrum is a straightforward approach leading to rather accurate IPs, (iv) the eigenvalue spectrum obtained with the so-called statistical average of different orbital model potential (SAOP) exchange-correlation model potential is an efficient approach leading directly to quite accurate IPs, and (v) a good prediction of the IP spectrum can be obtained from the shifted excitation spectra of the system calculated by the time-dependent DFT (TD-DFT) method. It is also shown that the TD-DFT calculations of the ionized species bring a significant improvement over the calculations of the neutral molecules, indicating that a great part of the electronic relaxation is already taken into account (in a similar way for all ionizations). Finally, in the case of TD-DFT calculations of neutral molecules, the statistical average of different orbital model potential (SAOP) functional does not lead to significantly better results than the B3LYP functional.

Importance of vibronic effects on the circular dichroism spectrum of dimethyloxirane

We present a theoretical study on the vibrational structure of a circular dichroism (CD) spectrum using time-dependent density-functional theory in combination with a Franck-Condon-type approach. This method is applied to analyze the complex CD spectrum of dimethyloxirane, which involves delicate cancellations of positive and negative CD bands. Our approach reveals that these cancellations are strongly affected by the shapes of the CD bands, and that it is vital for an accurate simulation of the spectrum to take the different envelopes of these bands into account. One crucial point in some former theoretical studies on this compound, which were restricted to vertical excitations, was the appearance of a strong negative CD band in the energy range of 7.0-7.5 eV, which is not present in the experimental spectrum. We can explain the disappearance of this 2B band by a strong vibrational progression along normal modes with C-O stretching character, so that the band extends over an energy range of almost 1.1 eV. Thus, it overlaps with many other (mostly positive) CD bands, leading to a cancellation of its intensity. The dominant vibrational features in the experimental spectrum can be assigned to the 1B, 3B, and 5B bands, which show several clear vibrational peaks and a total bandwidth of only 0.3-0.5 eV. In order to obtain close agreement between the simulated and the experimental spectrum we have to apply small shifts to the vertical excitation energies that enter the calculation. These shifts account both for possible errors in the time-dependent density-functional theory calculations and for the neglect of differential zero-point energy between ground and excited states in our gradient-based vertical Franck-Condon approach.

The merits of the frozen-density embedding scheme to model solvatochromic shifts

We investigate the usefulness of a frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] for the calculation of solvatochromic shifts. The frozen-density calculations, particularly of excitation energies have two clear advantages over the standard supermolecule calculations: (i) calculations for much larger systems are feasible, since the time-consuming time-dependent density functional theory (TDDFT) part is carried out in a limited molecular orbital space, while the effect of the surroundings is still included at a quantum mechanical level. This allows a large number of solvent molecules to be included and thus affords both specific and nonspecific solvent effects to be modeled. (ii) Only excitations of the system of interest, i.e., the selected embedded system, are calculated. This allows an easy analysis and interpretation of the results. In TDDFT calculations, it avoids unphysical results introduced by spurious mixings with the artificially too low charge-transfer excitations which are an artifact of the adiabatic local-density approximation or generalized gradient approximation exchange-correlation kernels currently used. The performance of the frozen-density embedding method is tested for the well-studied solvatochromic properties of the n-->pi(*) excitation of acetone. Further enhancement of the efficiency is studied by constructing approximate solvent densities, e.g., from a superposition of densities of individual solvent molecules. This is demonstrated for systems with up to 802 atoms. To obtain a realistic modeling of the absorption spectra of solvated molecules, including the effect of the solvent motions, we combine the embedding scheme with classical molecular dynamics (MD) and Car-Parrinello MD simulations to obtain snapshots of the solute and its solvent environment, for which then excitation energies are calculated. The frozen-density embedding yields estimated solvent shifts in the range of 0.20-0.26 eV, in good agreement with experimental values of between 0.19 and 0.21 eV.

Combined Theoretical and Experimental Deep-UV Resonance Raman Studies of Substituted Pyrenes

The results of time-dependent density functional theory (TDDFT) calculations of resonance Raman intensities are combined with experimental deep-ultraviolet resonance Raman measurements at a single wavelength, i.e., 244 nm, in order to test the possibility to distinguish several very similar compounds. Pyrene and three of its substituted derivatives, in which a single hydrogen atom has been replaced by a halogen atom, are compared. The fixed 244 nm excitation wavelength overlapped with the same electronic transition of the four pyrenes. Ground-state calculations using the BP86 exchange-correlation functional were used to predict the Raman frequencies, whereas excited-state calculations have been carried out employing the "statistical averaging of (model) orbital potentials" (SAOP) potential within a linear-response TDDFT framework in combination with the short-time approximation of resonance Raman intensities. In view of the simplistic theoretical approach, we find a surprisingly good agreement between the simulated and measured resonance Raman spectra of pyrene and its substituted analogues in terms of frequencies and intensities, which shows that the calculations can be used reliably to interpret the experimental spectra. With this combined information, it is possible to find criteria to distinguish the compounds under investigation, although many features of their vibrational spectra are similar.